If a circle has radius $r$, then an arc of $\alpha$ radians has length $r\alpha$. So with an infinitesimal increment $d\theta$ of the angle, the length is the infinitesimal $r\;d\theta$. And the arc is a right angles to the radius, which changes by the infinitesimal amount $dr$. So the infinitesimal area involved is just the product $r\;dr\;d\theta$.